document.write( "Question 690880: Find the sum of the first 196 terms of 2,7,12,17,.. I cant seem to figure this problem out \n" ); document.write( "

Algebra.Com's Answer #426421 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
If I say $\"+n+\"$ is the number of
\n" ); document.write( "the term of the sequence starting with zero, the
\n" ); document.write( "sequence looks like:
\n" ); document.write( " $\"+2+%2B+5%2A0+=+2+\"$
\n" ); document.write( " $\"+2+%2B+5%2A1+=+7+\"$
\n" ); document.write( " $\"+2+%2B+5%2A2+=+12+\"$
\n" ); document.write( " $\"+2+%2B+5%2A3+=+17+\"$
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\n" ); document.write( "To get 196 terms, I want to let $\"+n+\"$
\n" ); document.write( "run from $\"+0+\"$ to $\"+195+\"$
\n" ); document.write( "Summing up the terms as I started doing, I have:
\n" ); document.write( " $\"+2%2A196+\"$ + 5*( 0 + 1 + 2 + 3 + 4 + 5 + . . . + 195 )
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\n" ); document.write( "The only difficult thing here is the summation in the parentheses
\n" ); document.write( "I recall that $\"+1+%2B+2+%2B+3+%2B+4+%2B+5+%2B+6+%2B+7+%2B+8+%2B+9+%2B+10+=+%281%2F2%29%2A10%2A11+\"$
\n" ); document.write( "( check it out )
\n" ); document.write( "So your summation is $\"+%281%2F2%29%2A195%2A196+\"$
\n" ); document.write( " $\"+%281%2F2%29%2A195%2A196+=+%281%2F2%29%2A38220\"$
\n" ); document.write( " $\"+%281%2F2%29%2A38220+=+19110+\"$
\n" ); document.write( "Now I have
\n" ); document.write( " $\"+2%2A196+%2B+5%2A19110+\"$
\n" ); document.write( " $\"+392+%2B+95550+=+95942+\"$ answer
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\n" ); document.write( "I don't know any way to check the answer,
\n" ); document.write( "other than with some fancy calculator
\n" ); document.write( "or computer program.\r
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